LOWELL — There were 854 uniformed and undercover Boston police officers assigned on Marathon Monday to patrol the three miles from Cleveland Circle to Copley Square, many with their backs to the runners, scanning the crowd for potential threats.

State Police had nearly 1,000 troopers on the course from Hopkinton to the Back Bay, and the National Guard had about 200 soldiers helping out. Boston police, with help from transit officers, used specially trained dogs twice to sweep much of Boylston Street for explosives at 7 a.m. and then shortly before the elite runners approached the finish line.

With all the security on that pristine day in April, there was little authorities could have done to stop the Marathon bombings, Boston Police Commissioner Edward F. Davis said Tuesday at a counterterrorism forum at the University of Massachusetts Lowell, where he detailed the race’s massive security presence.

“There are not enough police officers in the Commonwealth of Massachusetts to lock down 26.2 miles of a marathon,” he said.

He added: “Everybody asks me what we could do to stop this. Do we need more cameras? Is there a computer system? Is there a piece of software to identify suspects? None of those things would work. They’re all helpful, but there is no magic bullet to deal with terrorism.”

Davis, who this week announced plans to leave his post in coming weeks, was among several speakers at the forum who participated in the response to the Marathon bombings, which left three people dead and more than 260 injured.

The forum coincided with a poll released by UMass Lowell’s new Center for Terrorism and Security Studies that found nearly two-thirds of Americans said they are more concerned about terrorism since the Marathon bombings and think the threats have increased over the past decade.

The survey by YouGov, which last month polled 1,000 people around the country, also found a majority said they think the United States is too involved in the affairs of other countries.

At the forum, Nicholas Rasmussen, deputy director of the National Counterterrorism Center in Washington, painted a bleak picture of the persistence of global terrorism, which he called “more dispersed and diffuse than any we’ve seen in the recent period of history.”

He said the dispersal of the threat from the Arabian Peninsula to the Horn of Africa has made fighting terrorists more of a challenge, especially as they provide instructions about how to build homemade bombs on the Internet.

“It’s a problem and a threat picture that stretches across the entire global landscape,” he said.

Rasmussen added that his chief concerns include Syria becoming a safe haven and launching pad for new Al Qaeda attacks, and the global reach of the network’s affiliates in Yemen. He called the group in Yemen the “most active, lethal, capable, and adaptive affiliate group and terrorist threat that we face right now. Particularly concerning, of course, is this affiliate group’s focus on homeland plotting.”

Vincent Lisi, special agent in charge of the FBI Boston division, said the Marathon bombings underscore why the United States must remain on alert, especially as federal, state, and local police forces shed officers.

“What they’ve done to us is exponentially increase the amount of people we have to worry about and the way they’re going to come at us,” he said. “The problem has become exponentially larger.”

He said the answer is not just to protect against what happened in previous attacks but to consider potential targets that might be considered implausible.

“We have to get ahead of the people who are constantly trying to exploit our vulnerabilities,” he said.

State Secretary of Public Safety Andrea Cabral, who was less than three months into her current job when Dzhokhar and Tamerlan Tsarnaev allegedly planted the two bombs on Boylston Street, said the response to the bombings represented an unprecedented level of cooperation between federal, state, and local authorities.

She noted that the amount of security at the Marathon and the large medical staff made a significant difference in limiting the number of deaths.

“There were things unique to that event that greatly aided our ability to respond,” she said, noting the bloody scene on Boylston Street was cleared within 18 minutes and that any victim who made it to an ambulance alive survived.

“It was all the training, all the preparation, and an excellent security plan that was in place going in . . . that made our response that much more effective,” she said.

She and others said the best way to avoid a future homegrown attack is through better policing, in which officers are more closely in touch with the community and learn about potential threats before they act.

But she said no matter how much is done to protect the public, there’s no way to inoculate a free society from committed terrorists.

“There will be more incidents, and yes, unfortunately, we will lose more people,” she said.